scholarly journals A Discontinuous Finite Volume Method for the Darcy-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhe Yin ◽  
Ziwen Jiang ◽  
Qiang Xu
Keyword(s):  
Error Estimate ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Numerical Examples ◽  
First Order ◽  
Theoretical Predictions ◽  
Volume Method

This paper proposes a discontinuous finite volume method for the Darcy-Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh-dependent norm. First-orderL2-error estimates are derived for the approximations of both velocity and pressure. Some numerical examples verifying the theoretical predictions are presented.

scholarly journals A Discrete Duality Finite Volume Method for Coupling Darcy and Stokes Equations

2019 ◽  
Vol 5 (1) ◽  
pp. 46-62
Author(s):  
M. Rhoudaf ◽  
N. Staïli
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Contact Interface ◽  
Numerical Examples ◽  
Lack Of Information ◽  
Darcy Problem ◽  
Darcy Equations ◽  
Normal Continuity ◽  
Volume Method

AbstractWe present a general finite volume method to solve a coupled Stokes-Darcy problem, we propose two domains corresponding to fluid region and porous region with a physical intersection. At the contact interface between the fluid region and the porous media we impose two conditions; the first one is the normal continuity of the velocity and the second one is the continuity of the pressure. Furthermore, due to the lack of information about both the velocity and the pressure on the interface, we will use Schwarz domain decomposition. In Darcy equations, the tensor of permeability will be considered as variable, since it depends on both the properties of the porous medium and the viscosity of the fluid. Numerical examples are presented to demonstrate the efficiency of the proposed method.

scholarly journals A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

2018 ◽  
Vol 40 (1) ◽  
pp. 405-421 ◽  
Author(s):  
N Chatterjee ◽  
U S Fjordholm
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Examples ◽  
Continuity Equations ◽  
Multiple Dimensions ◽  
Nonlocal Conservation Laws ◽  
Volume Method ◽  
Singular Data

Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

Analysis of a New Mixed Finite Volume Method

2003 ◽  
Vol 3 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Ilya D. Mishev
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Variable Pressure ◽  
Order Error ◽  
First Order ◽  
Scalar Variable ◽  
Volume Method ◽  
Well Posed ◽  
Theoretical Results

AbstractA new mixed finite volume method for elliptic equations with tensor coefficients on rectangular meshes (2 and 3-D) is presented. The implementation of the discretization as a finite volume method for the scalar variable (“pressure”) is derived. The scheme is well suited for heterogeneous and anisotropic media because of the generalized harmonic averaging. It is shown that the method is stable and well posed. First-order error estimates are derived. The theoretical results are confirmed by the presented numerical experiments.

A Hybrid Unstructured/Spectral Method for the Resolution of Navier-Stokes Equations

2009 ◽  
Author(s):  
Roque Corral ◽  
Javier Crespo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
The Third ◽  
Third Dimension ◽  
Volume Method

A novel high-order finite volume method for the resolution of the Navier-Stokes equations is presented. The approach combines a third order finite volume method in an unstructured two-dimensional grid, with a spectral approximation in the third dimension. The method is suitable for the resolution of complex two-dimensional geometries that require the third dimension to capture three-dimensional non-linear unsteady effects, such as those for instance present in linear cascades with separated bubbles. Its main advantage is the reduction in the computational cost, for a given accuracy, with respect standard finite volume methods due to the inexpensive high-order discretization that may be obtained in the third direction using fast Fourier transforms. The method has been applied to the resolution of transitional bubbles in flat plates with adverse pressure gradients and realistic two-dimensional airfoils.

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